Let's focus on the chart on the left for now: "Energy is gradually decoupling from economic growth."

Here's what this graph is showing: Ever since the 1970s, the world appears to be using less and less energy to produce a given unit of economic activity. Much of that has likely been achieved through technology — more fuel-efficient trucks, more efficient power plants, more energy-efficient manufacturing techniques. That allows us to do more with less.

One question is whether this trend will continue in the future. The analysts at BP are predicting the decoupling will accelerate in the next two decades: "Energy consumption grows less rapidly than the global economy," they note, "with GDP growth averaging 3.5% p.a. 2012-35. As a result energy intensity, the amount of energy required per unit of GDP, declines by 36% (1.9% p.a.) between 2012 and 2035."

There's some debate among economists, however, as to whether it's actually possible to significantly reduce the amount of energy used per unit of economic activity, as Steve Sorrell and David Ockwell of the University of Sussex explain in this overview essay (pdf). "Orthodox economists," they note, suggest that it's definitely possible to decouple the two: Energy appears to make only a small contribution to productivity. So it should be easy to replace energy inputs with either labor or capital (e.g., more efficient technology). There's no reason why we can't keep growing while using less and less energy per unit of GDP.

But as Sorrell and Ockwell note, many "ecological economists" dispute this. To them, the chart above is a bit of an illusion. The global economy hasn't become less dependent on energy. We've simply shifted to higher quality forms of energy over time. (For example, electricity is far more useful as an energy source than coal alone.) Once you adjust for quality, they'll say, then there actually hasn't been much in the way of decoupling. These economists also tend to emphasize the "rebound effect" — as society gets more energy-efficient, the cost of energy falls, and we'll just use more of it. Indeed, even BP's chart shows energy use continue to rise. (See here for more on the rebound debate.)

So why does this debate matter? Well, it matters a lot for climate-change policy. The growth rate of heat-trapping carbon-dioxide emissions in the future will depend on three things: 1) The growth rate of the global economy, 2) the energy-intensity of the economy (i.e., how much energy we need to sustain a given level of economic activity), and 3) the carbon-intensity of our energy supply (basically, the cleanliness of the fuels we use).

Right now, BP is predicting that the world's biggest countries will improve their energy intensity and carbon intensity in the next two decades. That is, they'll get more energy-efficient and use cleaner fuels (like boosting wind and solar, or switching from coal to natural gas, or shifting to electric vehicles):

But, the report notes, this also won't be enough to push down carbon-dioxide emissions, which BP sees rising considerably over the next two decades:

That "IEA 450 scenario" red line shows the path that carbon-dioxide emissions would have to take to meet climate goals. BP thinks we won't even get close, at least not on our current path.

There are three broad ways to cut emissions: Countries could ramp up their supplies of clean energy much faster than they're currently doing. As the chart at the very top shows, nuclear power and hydropower are expected to grow only slightly between now and 2035. Renewable energy (including biofuels) is expected to grow rapidly, but will still provide less than 10 percent of the world's primary energy. That's not nearly fast enough to cause global carbon emissions to drop.

The second option is that the world's economies could grow more slowly. That would put a dent in emissions. But no one really wants this option.

Second, the world's nations could try to do more to substantially reduce the amount of energy needed for a given unit of economic growth. As noted above, there's a lot of debate about whether this is even possible. (This is why, as Ockwell and Sorrell note, the "ecological economists" who cast doubt on decoupling tend to be the ones raising "fundamental questions about the long-term sustainability of economic growth.")

But for emissions to fall, some or all of those three trends would have to change from their current course.